Optimization problem under change of regime of interest rate

TL;DR

This paper investigates an optimization problem involving utility maximization of wealth and consumption in a market with sudden interest rate jumps, using BSDEs to analyze the dual and primal problems.

Contribution

It introduces a novel approach linking the dual problem's BSDE solution to the primal problem under interest rate regime changes.

Findings

Dual value function solves a BSDE

Duality links primal and dual problems

Interest rate jumps create market incompleteness

Abstract

In this paper, we study the classical problem of maximization of the sum of the utility of the terminal wealth and the utility of the consumption, in a case where a sudden jump in the risk-free interest rate creates incompleteness. The value function of the dual problem is proved to be solution of a BSDE and the duality between the primal and the dual value functions is exploited to study the BSDE associated to the primal problem.